Chapter 3, Problem 11Q

In a game held within a three-dimensional maze, you must move your game piece from start, at xyz coordinates (0, 0, 0), to finish, at coordinates (−2 cm, 4 cm, −4 cm). The game piece can undergo only the displacements (in centimeters) given below. It along the way, the game piece lands at coordinates (−5 cm, −1 cm, −1 cm) or (5 cm, 2 cm, −1 cm), you lose the game. Which displacements and in what sequence will get your game piece to finish?

$\begin{array}{l}\stackrel{\to }{p}=-7\hat{i}\text{ + 2}\hat{j}-3\hat{k}\stackrel{\to }{r}=2\hat{i}-\text{3}\hat{j}+2\hat{k}\\ \stackrel{\to }{q}=2\hat{i}-\hat{j}+4\hat{k}\stackrel{\to }{s}=3\hat{i}\text{ + 5}\hat{j}-3\hat{k}\end{array}$